DHC 161 2/28/12

Energy input strategiesInteraction between source and standing wave

Essential Features Review• Medium to support standing waves

– Harmonic series definite pitch– most common: strings or air-filled tubes

• Energy input strategy– Create (and sustain) the standing waves

• Amplification strategy– Strings require a soundboard and/or resonator– Wind instruments typically have a horn

• Pitch changing strategy– Almost always change the length of vibrating medium

• Practical to play– Problem of finger holes being too far apart

Strategies for sustaining standing waves

Almost contradictory requirements– Allow the medium to vibrate freely at its many natural

frequencies– Stimulate the standing waves that make those frequencies

Also make use of the fact that abrupt or discrete pulses generate many harmonics automatically

Use a method of “pushing” the medium that readily adapts to the standing wave frequencies

Solutions

stick-slip

Natural stick-slip frequency that depends on friction, applied force, and the relative motion of bow & string.

FeedbackThe stick-slip frequency will adjust to the frequency of the string’s vibration.

Bowed instruments

FeedbackInteraction between the standing

waves and the energy source

The source of vibration is usually weak and subtle.

It is easily influenced by the motion of the medium, itself.

The source will adjust its own frequency to match the natural frequency of a standing wave (usually the fundamental).

This adjustment & growth happens during the This adjustment & growth happens during the attackattack..

Vibrating reed

• Air flow between reeds causes gap to close (Bernoulli effect)• Restoring force of bent reeds causes gap to open again

Reeds oscillate due to blowing:

FeedbackPressure pulses from oscillating reeds are reflected from the end of the tube, travel back to the reed opening, and influence the opening and closing of the gap.

single reeds double reeds

Buzzing lips

Lips act like a pair of reeds

• Air flow through small gap between lips causes lips to close.

• Air being pushed from lungs forces lips open again.

• Feedback process is same as for reeds, but performer has

more control over lip tension than with reeds.

Edge toneAir blown past anedge naturally oscillates(vortex shedding)

Feedback If the edge is part of a tube, reflected pressure pulses will influence the timing of vortex shedding

flutes recorders

pan pipes

some organ pipes

Transient sound

• Amplitude decays for two main reasons1. Friction within vibrating medium and with air2. Sound radiates energy away

• Examples:– Plucked string– Tapped plate or membrane (drumhead)– Tapped tube of air– Handclap (sound comes from sudden change of

air pressure, which happens only once)

Sustained sound

1) Rate of energy applied is less than rate of energy leaked- vibration (and sound) amplitude will decrease

2) Rate of energy applied is equal to rate of energy leaked- amplitude will stay constant

3) Rate of energy applied is greater than rate of energy leaked- amplitude will increase

Regardless of the input mechanism, energy needs to be continually applied to the vibrating medium to replace energy that is “leaking” out

Energy in = Energy out

The rate of energy loss is proportional to amplitude.

Regardless of the level of energy input, the amplitude will grow until the rate of energy loss equals the rate of energy applied.

Most vibrating systems – including musical instruments – will reach a stable amplitude for a given amount of energy input. Such behavior is called self-limiting.

Why does this happen?

The faster and farther a string moves, the more work it does against the air (creating sound and friction)

The growth phase of a note played on a musical instrument is usually referred to as the attack

The AttackThe beginning of a sustained note during which...

synchronicity between vibration source and standing waves has not yet been established

the amplitude of standing waves is still growing